*Is everyone getting worked up about the cat going out at night or because OP said "kick the cat out" which I doubt she meant literally.
I've just put our cat out. She asks to go out almost every night except when it's torrential rain or freezing.*
But the OP doesn't say "I'm sick of the cat peeing on the tree/presents, she goes out regularly, including being out overnight, and she's begging to go out now, AIBU to leave her out until the morning?"
She just says she's kicking the cat out ... it's one thing if the cat is used to being out all night and/or being out in bad weather, but if it's only used to being out for a couple of hours, or in warmer weather then it's cruel to put the christmas tree over your cat's welfare.
I have two cats, one has always been a house cat but one was an indoor/outdoor cat who is now a house cat. She used to be my parents' who live in a semidetatched house, in a quiet cul-de-sac with large gardens but when I moved out into a terrace with busy roads on all sides so I didn't let her out for a good few weeks after I moved and she has turned into a very spoiled housecat who has no interest in going outside, except in summer when she likes to bask in the sun, but only in the back yard. If she went out all night when she was stil at my parents' she would be abslutely fine with that regardless of the conditions but now it would really upset her to be kicked out all night, especially in such cold/bad weather as we have tonight and she would be terrified.